Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting

Abstract

We present an efficient separation of variables algorithm for the evaluation of imaginary time Feynman diagrams appearing in the bold pseudo-particle strong coupling expansion of the Anderson impurity model. The algorithm uses a fitting method based on AAA rational approximation and numerical optimization to obtain a sum-of-exponentials expansion of the hybridization function, which is then used to decompose the diagrams. A diagrammatic formulation of the algorithm leads to an automated procedure for diagrams of arbitrary order and topology. We also present methods of stabilizing the self-consistent solution of the pseudo-particle Dyson equation. The result is a low-cost and high-order accurate impurity solver for quantum embedding methods using general multi-orbital hybridization functions at low temperatures, appropriate for low-to-intermediate expansion orders. In addition to other benchmark examples, we use our solver to perform a dynamical mean-field theory study of a minimal model of the strongly correlated compound Ca${}_2$RuO${}_4$, describing the anti-ferromagnetic transition and the in- and out-of-plane anisotropy induced by spin-orbit coupling.

arXiv comment22 pages. 7 figures

References in corpus (83)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Complexity in Strongly Correlated Electronic Systems
• Continuous-time Monte Carlo methods for quantum impurity models
• A continuous-time solver for quantum impurity models
• Strong electronic correlations from Hund's coupling
• Continuous Time Quantum Monte Carlo method for fermions
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
• The AAA algorithm for rational approximation
• TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
• Slave-rotor mean field theories of strongly correlated systems and the Mott transition in finite dimensions
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Orbital selective Mott transition in multi-band systems: slave-spin representation and dynamical mean-field theory
• Multi-band Gutzwiller wave functions for general on-site interactions
• Taming the dynamical sign problem in real-time evolution of quantum many-body problems
• Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Strongly Correlated Superconductivity: a plaquette Dynamical mean field theory study
• Rotationally-invariant slave-boson formalism and momentum dependence of the quasiparticle weight
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Nature of the Mott transition in Ca2RuO4
• Interplay of Mott Transition and Ferromagnetism in the Orbitally Degenerate Hubbard Model
• Spectral Properties of the Anderson Impurity Model, Comparison of Numerical Renormalization Group and Non--Crossing Approximation
• Electronic structure and magnetic properties of correlated metals: A local self-consistent perturbation scheme
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• Quantum impurity solvers using a slave rotor representation
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
• Hallmarks of Hund's coupling in the Mott insulator Ca${}_2$RuO${}_4$
• Mixing of $t_{2g}$-$e_g$ orbitals in 4d and 5d transition metal oxides
• Learning Feynman Diagrams with Tensor Trains
• Forces for Structural Optimizations in Correlated Materials within DFT+Embedded DMFT Functional Approach
• Efficient implementation of the Gutzwiller variational method
• Performance analysis of continuous-time solvers for quantum impurity models
• Discrete Lehmann representation of imaginary time Green's functions
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Chebyshev polynomial representation of imaginary time response functions
• Algorithmic Matsubara Integration for Hubbard-like models
• Observation of spin-orbit excitations and Hund's multiplets in Ca${}_2$RuO${}_4$
• Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids
• Emergent Bloch Excitations in Mott Matter
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Overcomplete compact representation of two-particle Green's functions
• Efficient hybridization fitting for dynamical mean-field theory via semi-definite relaxation
• Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
• Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations
• Real-frequency Diagrammatic Monte Carlo at Finite Temperature
• Legendre-spectral Dyson equation solver with super-exponential convergence
• A Tensor Train Continuous Time Solver for Quantum Impurity Models
• libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
• Solving the Bethe-Salpeter equation with exponential convergence
• Spectral functions of Sr${}_2$IrO${}_4$: theory versus experiment
• Quasi-Lindblad pseudomode theory for open quantum systems
• Properties of Gutzwiller wave-functions for multi-band models
• The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition
• Generalized slave-particle method for extended Hubbard models
• A fast time domain solver for the equilibrium Dyson equation
• Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited
• Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
• Pseudoparticle vertex solver for quantum impurity models
• Picosecond volume expansion drives a later-time insulator-metal transition in a nano-textured Mott Insulator
• Real-frequency response functions at finite temperature
• Fermi and non-Fermi liquid behavior in quantum impurity systems: Conserving slave boson theory
• Strong coupling impurity solver based on quantics tensor cross interpolation
• LIBAMI: Implementation of Algorithmic Matsubara Integration
• Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion
• Minimal pole representation for spectral functions
• Low rank Green's function representations applied to dynamical mean-field theory
• Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization
• Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models
• Chirped amplitude mode in photo-excited superconductors
• Inchworm quasi Monte Carlo for quantum impurities
• Discrete Lehmann representation of three-point functions
• Efficient Pseudomode Representation and Complexity of Quantum Impurity Models
• cppdlr: Imaginary time calculations using the discrete Lehmann representation
• Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
• Strong Coupling Quantum Impurity Solver on the Real and Imaginary Axes
• Solving quantum impurity models in the non-equilibrium steady state with tensor trains
• Computation Kernel for Feynman Diagrams
• High order strong-coupling expansion for X-ray absorption on a dynamically screened impurity